Question

How do you write `1/3x-1/3y=-2` in standard form and what is A, B, C?

Answer 1

`color(red)(1)x - color(blue)(1)y = color(green)(-6)`

Explanation:

The standard form of a linear equation is: `color(red)(A)x + color(blue)(B)y = color(green)(C)`

where, if at all possible, `color(red)(A)`, `color(blue)(B)`, and `color(green)(C)`are integers, and A is non-negative, and, A, B, and C have no common factors other than 1

To transform this equation into standard form we need to multiply each side of the equation by `color(red)(3)` which will also keep the equation balanced:

`color(red)(3)(1/3x - 1/3y) = color(red)(3) xx -2`

`(color(red)(3) xx 1/3x) - color(red)(3) xx 1/3y) = -6`

`3/3x - 3/3y = -6`

`1x - 1y = -6`